Class 8 Maths Chapter 1 Rational Numbers

NCERT Solutions for Class 8 Maths Chapter 1 Rational Numbers

Class 8 Maths Rational Numbers Exercise 1.1
Class 8 Maths Rational Numbers Exercise 1.2
Rational Numbers Class 8 Extra Questions

NCERT Solutions for Class 8 Maths Chapter 1 Rational Numbers Exercise 1.1

Ex 1.1 Class 8 Maths Question 1.
Using appropriate properties find:

Solution:

Ex 1.1 Class 8 Maths Question 2.
Write the additive inverse of each of the following:

(i) $\frac { 2 }{ 8 }$
(ii) $\frac { -5 }{ 9 }$
(iii) $\frac { -6 }{ -5 }$
(iv) $\frac { 2 }{ -9 }$
(v) $\frac { 19 }{ -6 }$

Solution:

Ex 1.1 Class 8 Maths Question 3.
Verify that -(-x) = x for
(i) x = $\frac { 11 }{ 5 }$
(ii) x = $\frac { -13 }{ 17 }$
Solution:

Ex 1.1 Class 8 Maths Question 4.
Find the multiplicative inverse of the following:

Solution:

Ex 1.1 Class 8 Maths Question 5.
Name the property under multiplication used in each of the following:

Solution:
(i) Commutative property of multiplication
(ii) Commutative property of multiplication
(iii) Multiplicative inverse property

Ex 1.1 Class 8 Maths Question 6.
Multiply $\frac { 6 }{ 13 }$ by the reciprocal of $\frac { -7 }{ 16 }$ .
Solution:

Ex 1.1 Class 8 Maths Question 7.
Tell what property allows you to compute

Solution:
Since a × (b × c) = (a × b) × c shows the associative property of multiplications.

Ex 1.1 Class 8 Maths Question 8.
Is $\frac { 8 }{ 9 }$ the multiplicative inverse of -1 $\frac { 1 }{ 8 }$ ? Why or Why not?
Solution:
Here -1 $\frac { 1 }{ 8 }$ = $\frac { -9 }{ 8 }$ .
Since multiplicative inverse of $\frac { 8 }{ 9 }$ is $\frac { 9 }{ 8 }$ but not $\frac { -9 }{ 8 }$
$\frac { 8 }{ 9 }$ is not the multiplicative inverse of -1 $\frac { 1 }{ 8 }$

Ex 1.1 Class 8 Maths Question 9.
If 0.3 the multiplicative inverse of 3 $\frac { 1 }{ 3 }$ ? Why or why not?
Solution:

Multiplicative inverse of 0.3 or $\frac { 3 }{ 10 }$ is $\frac { 10 }{ 3 }$ .
Thus, 0.3 is the multiplicative inverse of 3 $\frac { 1 }{ 3 }$ .

Ex 1.1 Class 8 Maths Question 10.
Write:
(i) The rational number that does not have a reciprocal.
(ii) The rational numbers that are equal to their reciprocals.
(iii) The rational number that is equal to its negative.
Solution:
(i) 0 is the rational number which does not have its reciprocal
[∵ $\frac { 1 }{ 0 }$ is not defined]
(ii) Reciprocal of 1 = $\frac { 1 }{ 1 }$ = 1
Reciprocal of -1 = $\frac { 1 }{ -1 }$ = -1
Thus, 1 and -1 are the required rational numbers.
(iii) 0 is the rational number which is equal to its negative.

Ex 1.1 Class 8 Maths Question 11.
Fill in the blanks.
(i) Zero has ……….. reciprocal.
(ii) The numbers ……….. and ……….. are their own reciprocals.
(iii) The reciprocal of -5 is ………
(iv) Reciprocal of $\frac { 1 }{ x }$ , where x ≠ 0 is ……….
(v) The product of two rational numbers is always a …………
(vi) The reciprocal of a positive rational number is ……….
Solution:
(i) no
(ii) -1 and 1
(iii) $\frac { -1 }{ 5 }$
(iv) x
(v) rational number
(vi) positive